It is known to employ a phase mask or phase grating in the Fourier plane of laser beam projection objects to modify the intensity profile of the laser beam at the image plane. Phase masks may modulate the amplitude (called transmission masks or gratings) or the phase (called pure phase masks) of the laser beam at the Fourier plane. The pure phase mask is actually a thin lens, often requiring a high order of surface curvature.
In applications where the laser power is limited, thin lens phase masks are preferred since they are 100% transmissive and do not reduce the intensity of the laser beam at the image plane. Pure phase masks may be formed as binary phase masks, where the thickness of transparent material forming the mask is varied in a step wise pattern, or continuous phase masks, where the thickness is varied smoothly. Methods for making binary phase masks are well known and straight forward. Because binary phase masks are easy to fabricate, they are generally preferred over continuously variable phase masks. For example, see the article "Spot Shaping and Incoherent Optical Smoothing for Raster Scanned Imagery," by Robert A. Gonsalves and Philip S. Considine, Optical Engineering, January-February 1976, Vol. 15, No. 1, page 64-67, where the authors chose to fabricate a binary phase mask because the ease of manufacture.
Recently, two of the present inventors have shown, through theoretical modeling studies of the beam shaping process, that an ideal spot intensity distribution can only be approximated using a binary phase mask, and that better results will be achieved with a thin lens continuous phase mask. See the article, "Modification of Laser Recording Beam for Image Quality Improvement," by J. Sullivan and L. Ray, Applied Optics, 1 May 1987, Vol. 26, No. 9, page 1765-17. In the article, the authors address the problem of modifying the intensity profile of a laser beam in a laser beam recorder to maximize the sharpness and minimize aliasing in a continuous tone image produced by the laser beam recorder. The use of a thin lens continuous phase mask to modulate the Gaussian amplitude of an inexpensive diode laser source would make it possible to use the diode laser to produce high quality images on fine grain photosensitive materials. As pointed out in the article, the minimum-error, two-dimensional spot intensity distribution for recording the sharpest digital image with minimal aliasing is a function of the image correlation, the discrete sampling lattice, and the temporal transfer function of the recorder. For a radially symmetric image correlation function of the form exp (-k.vertline.r.vertline.) (where k is a constant and r is radial distance), a square sampling grid, and a uniform temporal blur function in the line-scan direction, the minimun-error intensity distribution I(x,y) is as shown in FIG. 4, where the relative intensity is plotted against page and line scan directions in relative units of the sampling spacing .DELTA.. To achieve this intensity distribution with a diode laser having an ellipitical Gaussian intensity profile, the source distribution is phase modulated in the Fourier plane with a continuous phase mask.
FIG. 5 is a schematic diagram of a beam forming system employing a thin lens phase mask in the Fourier plane. The laser beam, illustrated by beam waists 10, is generated by a laser 12. The beam forming optics include a relay lens 14, and an objective lens 16 that forms an image of the input plane 19 onto an image plane 20. A phase mask 22 is positioned at the Fourier plane of the relay lens 14. The Fourier plane lies one focal distance from the relay lens 14. The phase mask 22 reshapes the beam intensity profile and modifies the beam waist as shown by dashed lines 10 prime in FIG. 5. With proper choice of the phase mask 22, the desired intensity profile of FIG. 4 is formed in the image plane.
For a continuous phase modulation .phi.(f.sub.x, f.sub.y) of finite extent the overall system transfer function is given by the modulus of the Fourier transform of the exposure distribution, which is given by the convolution of the intensity distribution and the line-scan temporal blur function, that is: EQU MTF(f.sub.x,f.sub.y)=.vertline.F{T(x).vertline.F.sup.-1 [e.sup.j.phi.(f.sbsp.x.sup.,f.sbsp.y.sup.) G(f.sub.x,f.sub.y)].vertline..sup.2 }.vertline. (1)
where f.sub.x is spatial frequency in the line-scan direction, f.sub.y is spatial frequency in the page-scan direction, G(f.sub.x,f.sub.y) is the Fourier transform of the source amplitude distribution g(x,y), T(x) is the temporal transfer function, and F represents Fourier transformation. The squared error between this transfer function and the desired transfer function defined by the Fourier transfer of the minimum-error intensity distribution and the line-scan blur function is minimized by choosing the appropirate phase modulation. For even, polynomial phase, the resultant two-dimensional phase profile is smooth and, therefore, can be realized by thickness variations in optically transmissive material with an index of refraction that is different than that of air (i.e. by a thin lens of high order curvature). FIG. 6 shows the phase profile of a continuous phase mask for shaping a laser beam having an elliptical Gaussian profile to the intensity profile of FIG. 4.
Physical realization of the desired phase profile for the thin lens continuous phase mask prevents a problem, since the higher order curvature requirements (e.g. beyond second order) for extreme phase manipulation preclude techniques such as conventional optical grinding. Furthermore, plastic injection molding does not provide the subtle thickness variations (within .lambda./8) over the small areas that phase manipulation requires (typical mask dimensions are 5.times.5 mm square).
It is therefore an object of the present invention to provide an improved method of making a thin lens, and particularly a thin lens continuous phase mask for laser spot shaping. It is a further object of the invention to provide such a method capable of producing continuous optical surfaces having third and higher order curvatures.